Hide some tasks only a few hours into the future

How can I hide a task that is due today, but not until a specific future time e.g. right now it's noon and it's due at 5pm? Let's say I want to remind myself to take a medication. I'd rather not even see that task until it comes due. Any way to accomplish that?

Edited to add a note: Most tasks aren't like this, and it's actually beneficial to see them in the future so I can plan for them, do them early, etc. It's really on a task-by-task basis that I'd like this hiding ability.